High-order implicit time integration for unsteady incompressible flows

Author (s): Montlaur, A.; Fernández-Méndez, S. and Huerta, A.
Journal: International Journal for Numerical Methods in Fluids

Volume: 70, Issue 5
Pages: 603 – 626
Date: 2012

Abstract:
The spatial discretization of unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge-Kutta and Rosenbrock methods applied to the solution of the resulting index-2 DAE system is analyzed. A critical comparison of Rosenbrock, semi-implicit and fully implicit Runge-Kutta methods is performed, in terms of order of convergence and stability. Numerical examples, considering a Discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approaches, and compare their performance with classical methods for incompressible flows.

Journal paper (from the publisher)  
UPCommons page Link  

Bibtex:

@article{ADM-MFH:12,
	Author = {Montlaur, Adeline and Fern{{\'a}}ndez-M{{\'e}}ndez, Sonia and Huerta, Antonio},
	Title = {High-order implicit time integration for unsteady incompressible flows},
	Fjournal = {International Journal for Numerical Methods in Fluids},
	Journal = {Internat. J. Numer. Methods Fluids},
	Volume = {70},
	Number = {5},
	Pages = {603--626},
	Year = {2012},
	Doi = {10.1002/fld.2703},
	Url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.2703/pdf}
	}